Question

Explain why the rate of change of the radius of the sphere is not constant even though dV/dt is constant. dr dt depends on r2, not simply r. The volume only appears constant; it is actually a rational relationship. The rate of change of the radius is a linear relationship whose slope is dV dt . The rate of change of the radius is a cubic relationship. dr dt as a function runs parallel to the volume function, which is not linear.

Answer 1

Hello your question has some missing parts below is the missing part

A spherical balloon is inflated with gas at a rate of 600 cubic centimeters per minute

answer :

• dr/dt depends on r^2 not simply r

Explanation:

The rate of change of the radius of the sphere is not constant even though dv/dt is constant is because ;

• dr/dt depends on r^2 not simply r

and this is because dr/dt is proportional to 1/r^2 therefore the rate of change of the radius cannot be constant even though dv/dt is constant